This excerpt is taken from Sheikh Abu Hamza Abdul Khaliq Siddiqi's book Sahih Fazail-e-Amaal.
عن عبد الله بن عمرو بن العاص رضي الله عنهما أنه سمع النبى صلى الله عليه وسلم يقول: إذا سمعتم المؤذن فقولوا مثل ما يقول، ثم صلوا على ، فإنه من صلى على صلاة صلى الله عليه بها عشرا، ثم سلوا الله لي الوسيلة ، فإنها منزلة فى الجنة لا تنبغي إلا لعبد من عباد الله وأرجو أن أكون أنا هو، فمن سأل لي الوسيلة حلت عليه الشفاعة .
Our master Abdullah bin Umar (may Allah be pleased with them) narrates that he heard the Prophet Muhammad (peace be upon him) say: "When you hear the Adhan, say it as the Mu'adhdhin says, then send blessings upon me, for whoever sends blessings upon me once, Allah sends ten blessings upon him. Then ask Allah to grant me intercession, for indeed it is a high rank in Paradise, which is only worthy of one servant among Allah's servants, and I hope that that servant is me. So whoever asks for my intercession, intercession will be permissible for him."
Reference: Sahih Muslim, Book of Prayer, Chapter on the recommendation to say what the Mu'adhdhin says, Hadith number: 384.
عن عمر بن الخطاب رضى الله عنه قال قال رسول الله صلى الله عليه وسلم: إذا قال المؤذن: الله أكبر الله أكبر ، فقال أحدكم: الله أكبر الله أكبر . ثم قال: أشهد أن لا إله إلا الله، قال: أشهد أن لا إله إلا الله . ثم قال: أشهد أن محمدا رسول الله ، قال: أشهد أن محمدا رسول الله . ثم قال: حي على الصلاة، قال: لا حول ولا قوة إلا بالله ، ثم قال: حي على الفلاح ، قال: لا حول ولا قوة إلا بالله . ثم قال: الله أكبر الله أكبر، قال: الله أكبر الله أكبر. ثم قال: لا إله إلا الله ، قال: لا إله إلا الله، من قلبه دخل الجنة .
It is narrated from our master Umar bin Khattab (may Allah be pleased with him) that the Messenger of Allah (peace be upon him) said: When the Mu'adhdhin says الله اكبر الله اكبر and one of you responds by saying __ARABIC_3. Then the Mu'adhdhin says ARABIC_4__ and he says __ARABIC_5. Then the Mu'adhdhin says ARABIC_6__ and he says __ARABIC_7. Then the Mu'adhdhin says ARABIC_8__ and he says __ARABIC_9. Then the Mu'adhdhin says ARABIC_10__ and he says __ARABIC_11. Then the Mu'adhdhin says ARABIC_12__ and he says __ARABIC_13. Then the Mu'adhdhin says ARABIC_14__ and he says لا إله إلا الله. (If he says all these words) from the heart, he will enter Paradise.
Reference: Sahih Muslim, also, Hadith number: 385.
① The first supplication of the Adhan:
اللَّهُمَّ صَلِّ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ، كَمَا صَلَّيْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌ، اللَّهُمَّ بَارِكْ عَلَى مُحَمَّدٍ وَعَلَى آلِ مُحَمَّدٍ، كَمَا بَارَكْتَ عَلَى إِبْرَاهِيمَ وَعَلَى آلِ إِبْرَاهِيمَ، إِنَّكَ حَمِيدٌ مَجِيدٌ
"O Allah! Send mercy upon Muhammad, peace be upon him, and the family of Muhammad, just as You sent mercy upon Ibrahim, peace be upon him, and the family of Ibrahim. Praise and greatness are for You alone, O Allah! Send blessings upon Muhammad, peace be upon him, and the family of Muhammad, just as You sent blessings upon Ibrahim and the family of Ibrahim. Praise and greatness are for You alone."
② The second supplication of the Adhan:
اللَّهُمَّ رَبَّ هَذِهِ الدَّعْوَةِ التَّامَّةِ، وَالصَّلَاةِ الْقَائِمَةِ، آتِ مُحَمَّدًا الْوَسِيلَةَ وَالْفَضِيلَةَ، وَابْعَثْهُ مَقَامًا مَحْمُودًا الَّذِي وَعَدْتَهُ
"O Allah! The Lord of this (Tawheed) complete call and the established prayer, grant Muhammad, peace be upon him, the means, greatness, and the Praiseworthy Station which You have promised him."
Reference: Sahih Bukhari, Book of Adhan, Chapter: Supplication at the call, Number: 614
③ The third supplication of the Adhan:
رَضِيتُ بِاللَّهِ رَبًّا، وَبِالْإِسْلَامِ دِينًا، وَبِمُحَمَّدٍ ﷺ نَبِيًّا
"I am pleased with Allah as my Lord, with Islam as my religion, and with Muhammad, peace be upon him, as my Prophet."
Reference: Sahih Muslim, Book of Prayer, Chapter: Saying like the Mu'adhdhin's saying, Number: 386.